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О линейной независимости совокупностей значений рядов с периодическими коэффициентами
С. 129–130.
Language:
Russian
In book
Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2024.
Nesterenko A., Чирский В. Г., Чебышевский сборник 2025 Т. 26 № 4 С. 460–465
We consider sets of integers $a_{n}^{(k,j)}, j=1,...,m, k=1,...,T_{j}$ which satisfy conditions $$a_{n}^{(k,j)}=a_{n+T_{j}}^{(k,j)} ,j=1,...,m, k=1,...,T_{j}, n=0,1,... $$ and functions
$$F_{j,k}(z)=\sum_{n=0}^{\infty}\frac{a_{n}^{(k,j)}}{n!}z^{n}, j=1,...,m, k=1,...,T_{j}. $$ We find conditions under which the set of functions $$ 1, e^{z}, F_{j,k}(z), j=1,...,m, k=2,...,T_{j} $$
is linearly independent over $ \mathbb{C} (z) $ and for any rational $ \gamma\neq 0 $ their values at ...
Added: March 3, 2026
Barash L., Guskova M., Shchur L., Программирование 2017 № 3 С. 22–40
By the example of the RNGAVXLIB random number generator library, this paper considers some approaches to employing AVX vectorization for calculation speedup. The RNGAVXLIB library contains AVX implementations of modern generators and the routines allowing one to initialize up to 10^19 independent random number streams. The AVX implementations yield exactly the same pseudorandom sequences as the ...
Added: October 4, 2018
Guskova M., Barash L., Shchur L., Труды Института системного программирования РАН 2018 Т. 30 № 1 С. 115–126
The generation of uniformly distributed random numbers is necessary for computer simulation by Monte Carlo methods and molecular dynamics. Generators of pseudo-random numbers (GPRS) are used to generate random numbers. GPRS uses deterministic algorithms to calculate numbers, but the sequence obtained in this way has the properties of a random sequence. For a number of ...
Added: March 26, 2018
Nesterenko A., Ученые записки Орловского государственного университета. Серия: Естественные, технические и медицинские науки 2012 № 6 С. 170–176
Предложен подход к генерации асевдослучайных последовательностей, основанный на представлениях одного класса действительных чисел. Описаны алгоритм генерации, результаты практических вычислений, а также дана методика тестирования полученных последовательностей. ...
Added: January 20, 2018
Бараш Л. Ю., Shchur L., Cuda Альманах 2014 № 3 С. 17–17
Libraries RNGSSELIB и PRAND for the parallel generation of pseudo-random numbers in Monte Carlo simulations was developed. RNGSSELIB library contains realization based on the SSE extensionin the modern CPU, and PRAND library contains the generators using CUDA version 5.0 and later. ...
Added: March 10, 2016
Enatskaya N., Khakimullin E. R., М.: Московский государственный институт электроники и математики, 2012.
В пособии рассмотрены вопросы получения и проверки качестве псевдослучайных чисел (ПСЧ) для их дальнейшего использования в стохастическом моделировании.
Рекомендовано студентам ФПМ для выполнения курсовых и дипломных работ. ...
Added: March 13, 2015
Barash L. Y., L. N. Shchur, Computer Physics Communications 2011 Vol. 182 P. 1518–1527
The library RNGSSELIB for random number generators (RNGs) based upon the SSE2 command set is presented. The library contains realization of a number of modern and most reliable generators. Usage of SSE2 command set allows to substantially improve performance of the generators. Three new RNG realizations are also constructed. We present detailed analysis of the ...
Added: March 25, 2014
Barash L. Y., Shchur L., Computer Physics Communications 2014 Vol. 185 P. 1343–1353
The library PRAND for pseudorandom number generation for modern CPUs and GPUs is presented. It contains both single-threaded and multi-threaded realizations of a number of modern and most reliable generators recently proposed and studied in Barash (2011), Matsumoto and Tishimura (1998), L’Ecuyer (1999,1999), Barash and Shchur (2006) and the efficient SIMD realizations proposed in Barash ...
Added: March 22, 2014
Barash L. Y., L.N. Shchur, Computer Physics Communications 2013 Vol. 184 No. 10 P. 2367–2369
In this update, we present the new version of the random number generator (RNG) library RNGSSELIB,which, in particular, contains fast SSE realizations of a number of modern and most reliable generators [1]. The new features are: (i) Fortran compatibility and examples of using the library in Fortran; (ii) new modern and reliable generators; (iii) the ...
Added: March 17, 2014